An oil supply system for an engine includes a pump body provided with a first outlet port and a second outlet port. The oil supply system further includes a hydraulic-oil-delivery passage, a first oil passage, a second oil passage and a return hydraulic passage. The valve body divides a hydraulic-oil receiving portion for receiving the hydraulic oil in the hydraulic-pressure control valve chamber into a first valve chamber and a second valve chamber. When the hydraulic pressure oil delivered to the hydraulic-oil-delivery passage is in a predetermined value, the hydraulic oil discharged out of the second outlet port is delivered to the hydraulic-oil-delivery passage via the first valve chamber. When the hydraulic pressure delivered to the hydraulic-oil-delivery passage exceeds the predetermined value, the hydraulic oil discharged out of the second outlet port is delivered to the hydraulic-oil-delivery passage via the second valve chamber.